Chelsea are currently in the market for a new centre-forward after it was revealed that head coach Antonio Conte had told Spain international Costa that he was surplus to requirements ahead of the 2017-18 campaign.
Lukaku has been strongly linked with a return to the club that he left in 2014, and Cole has insisted that he would "take" the Belgian if he were in control of matters.
"Obviously the Costa thing has come out. Conte has told him that he wants him out so you would be looking at a striker," Cole told Goal.com.
"Lukaku, there's a market for him, and you are competing for players. I like Lukaku. I'd take Lukaku, he is like for like with Costa, but they only need one or two players and just keep the continuity going.
"I don't know his character so it is hard to say [whether the comeback could affect him], but I would say is that the pressure is different when you play for Chelsea, rather than Everton. He is younger [than Costa], that's in his favour."
Cole, who represented Chelsea between 2003 and 2010, currently plays his football in Florida with the Tampa Bay Rowdies.